]> 2008/06/10 OpenCyc Knowledge Base Copyright© 2001-2008 Cycorp, Inc., http://www.cyc.com/, Austin, TX, USA This file contains an OWL representation of information contained in the OpenCyc Knowledge Base. The content of this OWL file is licensed under the Creative Commons Attribution 3.0 license whose text can be found at http://creativecommons.org/licenses/by/3.0/legalcode. The content of this OWL file, including the OpenCyc content it represents, constitutes the "Work" referred to in the Creative Commons license. The terms of this license equally apply to, without limitation, renamings and other logically equivalent reformulations of the content of this OWL file (or portions thereof) in any natural or formal language, as well as to derivations of this content or inclusion of it in other ontologies. externalID A unique, language-neutral, variable-sized identifier for a concept that can be used to refer unambiguously to that concept across OWL exports or across Cyc inference engines. label A natural-language representation for a concept that is both human readable and readable by the Cyc inference engine. These terms are not guaranteed to refer to the same concept across time but are guaranteed to be consistent within a particular OWL export. Use 'cycAnnot:externalID' for unambiguously referring to a concept across OWL exports or across Cyc inference engines. A collection of collections. Every instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rbEngJGwWEdqAAAACs71DGQ" class="cyc_term">CollectionClosedUnderSpecialization</a> is a collection <code>COLL-TYPE</code> with the following property: If the collection <code>COLL</code> is an instance of <code>COLL-TYPE</code>, then for any specialization <code>SPEC</code> of <code>COLL</code>, <code>SPEC</code> is also an instance of <code>COLL-TYPE</code>. Notable examples include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVitN5wpEbGdrcN5Y29ycA" class="cyc_term">TemporalStuffType</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAzJwpEbGdrcN5Y29ycA" class="cyc_term">Collection</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViA9JwpEbGdrcN5Y29ycA" class="cyc_term">Thing</a>. collection closed under specialization CollectionClosedUnderSpecialization A collection of collections, and a specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjatpwpEbGdrcN5Y29ycA" class="cyc_term">RelationshipType</a>. Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViI_pwpEbGdrcN5Y29ycA" class="cyc_term">PredicateType</a> is a collection of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViA1pwpEbGdrcN5Y29ycA" class="cyc_term">Predicate</a>s. The predicates in a given predicate category represented in the Knowledge Base are typically those sharing some common feature(s) considered significant enough that the collection of all such predicates is useful to reify. Although what constitutes a "significant common feature" is difficult to specify precisely, there are many clear-cut cases. Instances of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViI_pwpEbGdrcN5Y29ycA" class="cyc_term">PredicateType</a> include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViDSpwpEbGdrcN5Y29ycA" class="cyc_term">TemporalPartPredicate</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViBYpwpEbGdrcN5Y29ycA" class="cyc_term">QuantitySlot</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViBpJwpEbGdrcN5Y29ycA" class="cyc_term">FunctionalSlot</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjwkZwpEbGdrcN5Y29ycA" class="cyc_term">InterActorSlot</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjJFpwpEbGdrcN5Y29ycA" class="cyc_term">TransitiveBinaryPredicate</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViUdZwpEbGdrcN5Y29ycA" class="cyc_term">PropositionalAttitudeSlot</a>. See also the comment on <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViA1pwpEbGdrcN5Y29ycA" class="cyc_term">Predicate</a>. predicate category PredicateType type of collection type CollectionTypeType A higher-order collection and an instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNs-F0CChEdaAAABQ2rksLw" class="cyc_term">VariedOrderCollection</a>. Instances of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rviPYH5wpEbGdrcN5Y29ycA" class="cyc_term">CollectionTypeType</a> are types of collection types, that is, collections whose instances are collections of (not necessarily first-order) collections. Thus any instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNooX_CChEdaAAABQ2rksLw" class="cyc_term">FixedOrderCollection</a> (q.v.) of order greater than or equal to 3 is a specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rviPYH5wpEbGdrcN5Y29ycA" class="cyc_term">CollectionTypeType</a>. fixed-order Cyc collection A <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvtppU5wpEbGdrcN5Y29ycA" class="cyc_term">CollectionType</a> and the collection of all and only those <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAzJwpEbGdrcN5Y29ycA" class="cyc_term">Collection</a>s whose own instances are all of the same fixed "order", where order is understood as follows. Let individuals (i.e. instances of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjaApwpEbGdrcN5Y29ycA" class="cyc_term">Individual</a>) be "zeroth-order" things, collections of (only) individuals "first-order" collections, ..., and collections of (only) <code>N</code>th-order things "<code>(N</code>+1)th-order" collections. More precisely, then, a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAzJwpEbGdrcN5Y29ycA" class="cyc_term">Collection</a> <code>COL</code> is a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNooX_CChEdaAAABQ2rksLw" class="cyc_term">FixedOrderCollection</a> if and only if it is an <code>N</code>th-order collection (for <code>N</code> >= 1). Instances of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNooX_CChEdaAAABQ2rksLw" class="cyc_term">FixedOrderCollection</a> include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjaApwpEbGdrcN5Y29ycA" class="cyc_term">Individual</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHIBS0h_TEdaAAABQ2rksLw" class="cyc_term">FirstOrderCollection</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHQdVmB_TEdaAAABQ2rksLw" class="cyc_term">SecondOrderCollection</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHUFI8h_TEdaAAABQ2rksLw" class="cyc_term">ThirdOrderCollection</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHM37Dh_TEdaAAABQ2rksLw" class="cyc_term">FourthOrderCollection</a>, and all specializations of these. Specializations of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNooX_CChEdaAAABQ2rksLw" class="cyc_term">FixedOrderCollection</a> include all of the preceding examples except <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjaApwpEbGdrcN5Y29ycA" class="cyc_term">Individual</a> and its specializations. Note that any #$quotedCollection (q.v.) is a fixed-order collection, since all of its instances are CycL expressions. Thus (e.g.) <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvZczwpwpEbGdrcN5Y29ycA" class="cyc_term">CycLDenotationalTerm</a> is fixed-order. It would be a mistake to infer, from the fact that the instances of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvZczwpwpEbGdrcN5Y29ycA" class="cyc_term">CycLDenotationalTerm</a> happen to denote things of different orders, that this collection is itself not of fixed-order. An example of a collection that is not fixed-order is <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rpJ-nSEkJQdeC8NLkYPDBBw" class="cyc_term">AbstractThing</a>, which is a varied-order collection since it contains both (zeroth-order) abstract individuals and (first-and-higher-order) collections. Note that, although they are mutually disjoint, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNooX_CChEdaAAABQ2rksLw" class="cyc_term">FixedOrderCollection</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNs-F0CChEdaAAABQ2rksLw" class="cyc_term">VariedOrderCollection</a> (q.v.) do not constitute a partition of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAzJwpEbGdrcN5Y29ycA" class="cyc_term">Collection</a>: since the notion of order described above is not applicable to sets, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvl2en5wpEbGdrcN5Y29ycA" class="cyc_term">Set_Mathematical</a> (e.g.) and its specializations are neither fixed-order nor varied-order collections. FixedOrderCollection The collection of all specializations of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHIBS0h_TEdaAAABQ2rksLw" class="cyc_term">FirstOrderCollection</a>, that is, of all collections of (first-order) collections, and an instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHUFI8h_TEdaAAABQ2rksLw" class="cyc_term">ThirdOrderCollection</a>. Instances of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHQdVmB_TEdaAAABQ2rksLw" class="cyc_term">SecondOrderCollection</a> are collections of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHIBS0h_TEdaAAABQ2rksLw" class="cyc_term">FirstOrderCollection</a>s. Any instance of any instance of any instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHQdVmB_TEdaAAABQ2rksLw" class="cyc_term">SecondOrderCollection</a> is an <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjaApwpEbGdrcN5Y29ycA" class="cyc_term">Individual</a>. SecondOrderCollection second-order Cyc collection A collection of collections of collections. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvtppU5wpEbGdrcN5Y29ycA" class="cyc_term">CollectionType</a> is the collection of all (and only) types of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAzJwpEbGdrcN5Y29ycA" class="cyc_term">Collection</a>s. More precisely, a thing COLLTYPE is an instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvtppU5wpEbGdrcN5Y29ycA" class="cyc_term">CollectionType</a> if and only if COLLTYPE is a non-empty collection all of whose instances are collections. Example: <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwPzQbJwpEbGdrcN5Y29ycA" class="cyc_term">PersonTypeByCulture</a>, each of whose instances is the collection of all persons who participate in some particular human culture, is an instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvtppU5wpEbGdrcN5Y29ycA" class="cyc_term">CollectionType</a>. Important specializations of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvtppU5wpEbGdrcN5Y29ycA" class="cyc_term">CollectionType</a> include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvWPoRpwpEbGdrcN5Y29ycA" class="cyc_term">DisjointCollectionType</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViA4pwpEbGdrcN5Y29ycA" class="cyc_term">SiblingDisjointCollectionType</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rviPYH5wpEbGdrcN5Y29ycA" class="cyc_term">CollectionTypeType</a>. CollectionType type of collection thing Thing <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViA9JwpEbGdrcN5Y29ycA" class="cyc_term">Thing</a> is the "universal collection": the collection which, by definition, contains everything there is. Every thing in the Cyc ontology -- every <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjaApwpEbGdrcN5Y29ycA" class="cyc_term">Individual</a> (of any kind), every <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvl2en5wpEbGdrcN5Y29ycA" class="cyc_term">Set_Mathematical</a>, and every <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAzJwpEbGdrcN5Y29ycA" class="cyc_term">Collection</a> -- is an instance of (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViBBJwpEbGdrcN5Y29ycA" class="cyc_term">isa</a>) <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViA9JwpEbGdrcN5Y29ycA" class="cyc_term">Thing</a>. Similarly, every collection is a subcollection of (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViBDpwpEbGdrcN5Y29ycA" class="cyc_term">genls</a>) <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViA9JwpEbGdrcN5Y29ycA" class="cyc_term">Thing</a>. Trivially, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViA9JwpEbGdrcN5Y29ycA" class="cyc_term">Thing</a> is both an instance of and a subcollection of itself, and is not a subcollection of any other collection. (Note that the above reference to "every thing in the Cyc ontology" is not meant to be limited to things actually reified in the Cyc system, but includes (e.g.) every instance -- reified or not, known or not -- of every collection recognized by Cyc.) FunctionType type of function A collection of collections that is a specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjatpwpEbGdrcN5Y29ycA" class="cyc_term">RelationshipType</a>. Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rv_hDCJwpEbGdrcN5Y29ycA" class="cyc_term">FunctionType</a> is a collection of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVxAsJwpEbGdrcN5Y29ycA" class="cyc_term">Function_Denotational</a>s. The functions in a given function-category represented in the Knowledge Base are typically those sharing some common feature(s) -- often having to do with what kind of thing the functions return (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViA8ZwpEbGdrcN5Y29ycA" class="cyc_term">resultIsa</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjWq5wpEbGdrcN5Y29ycA" class="cyc_term">resultGenl</a>s) -- considered significant enough that the collection of all such functions is useful to reify. Although what constitutes a "significant common feature" is difficult to specify precisely, there are many clear-cut cases. Examples include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVj62ZwpEbGdrcN5Y29ycA" class="cyc_term">IndividualDenotingFunction</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAapwpEbGdrcN5Y29ycA" class="cyc_term">CollectionDenotingFunction</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwAUw9JwpEbGdrcN5Y29ycA" class="cyc_term">FunctionDenotingFunction</a>. See also <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViI_pwpEbGdrcN5Y29ycA" class="cyc_term">PredicateType</a>. fourth-order Cyc collection FourthOrderCollection An instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNooX_CChEdaAAABQ2rksLw" class="cyc_term">FixedOrderCollection</a> and a specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rviPYH5wpEbGdrcN5Y29ycA" class="cyc_term">CollectionTypeType</a>. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHM37Dh_TEdaAAABQ2rksLw" class="cyc_term">FourthOrderCollection</a> is the collection of all specializations of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHUFI8h_TEdaAAABQ2rksLw" class="cyc_term">ThirdOrderCollection</a>. A notable instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHM37Dh_TEdaAAABQ2rksLw" class="cyc_term">FourthOrderCollection</a> is <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHUFI8h_TEdaAAABQ2rksLw" class="cyc_term">ThirdOrderCollection</a>. third-order Cyc collection ThirdOrderCollection An instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHM37Dh_TEdaAAABQ2rksLw" class="cyc_term">FourthOrderCollection</a> and a specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rviPYH5wpEbGdrcN5Y29ycA" class="cyc_term">CollectionTypeType</a>. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHUFI8h_TEdaAAABQ2rksLw" class="cyc_term">ThirdOrderCollection</a> is the collection of all specializations of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHQdVmB_TEdaAAABQ2rksLw" class="cyc_term">SecondOrderCollection</a> (q.v.). Notable instances of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHUFI8h_TEdaAAABQ2rksLw" class="cyc_term">ThirdOrderCollection</a> include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHQdVmB_TEdaAAABQ2rksLw" class="cyc_term">SecondOrderCollection</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViNxpwpEbGdrcN5Y29ycA" class="cyc_term">BiologicalTaxonType</a>. A collection of collections. Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvWXYgJwpEbGdrcN5Y29ycA" class="cyc_term">ExistingObjectType</a> is a specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVj27ZwpEbGdrcN5Y29ycA" class="cyc_term">PartiallyTangible</a> (q.v.). Moreover, each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvWXYgJwpEbGdrcN5Y29ycA" class="cyc_term">ExistingObjectType</a> is a collection that is temporally stuff-like (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVitN5wpEbGdrcN5Y29ycA" class="cyc_term">TemporalStuffType</a>) but physically-spatially object-like (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVirnZwpEbGdrcN5Y29ycA" class="cyc_term">ObjectType</a>) -- i.e. object-like with respect to some physical-spatial part-whole predicate (e.g. some specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r8a2smPXcQdiEoJhcx65EiQ" class="cyc_term">properPhysicalDecompositions</a>). Consider the collection <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwJaXepwpEbGdrcN5Y29ycA" class="cyc_term">BookCopy</a>. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwJaXepwpEbGdrcN5Y29ycA" class="cyc_term">BookCopy</a> is a specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVj27ZwpEbGdrcN5Y29ycA" class="cyc_term">PartiallyTangible</a>. Further, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwJaXepwpEbGdrcN5Y29ycA" class="cyc_term">BookCopy</a> is temporally stuff-like: any one of the <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvWn4OZwpEbGdrcN5Y29ycA" class="cyc_term">timeSlices</a> of a given copy <code>COPY</code> of (say) "Moby Dick" is still a copy of "Moby Dick". (Most collections of tangible objects are temporally stuff-like in this way.) But <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwJaXepwpEbGdrcN5Y29ycA" class="cyc_term">BookCopy</a> is spatially object-like: if we take a scalpel and slice <code>COPY</code> into ten pieces, each piece is not a copy of "Moby Dick". So <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwJaXepwpEbGdrcN5Y29ycA" class="cyc_term">BookCopy</a> is an instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvWXYgJwpEbGdrcN5Y29ycA" class="cyc_term">ExistingObjectType</a>. See also <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVir35wpEbGdrcN5Y29ycA" class="cyc_term">StuffType</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVny6pwpEbGdrcN5Y29ycA" class="cyc_term">ExistingStuffType</a>. ExistingObjectType type of object A collection of collections. Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjatpwpEbGdrcN5Y29ycA" class="cyc_term">RelationshipType</a> is a collection of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAzZwpEbGdrcN5Y29ycA" class="cyc_term">Relation</a>s. The relations in a given relationship-type represented in the Knowledge Base are typically those sharing some common feature(s) -- often having to do with what kinds of things the relations relate (see e.g. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvuItPZwpEbGdrcN5Y29ycA" class="cyc_term">argIsa</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvyTLHJwpEbGdrcN5Y29ycA" class="cyc_term">argGenl</a>s) -- considered significant enough that the collection of all such relations is useful to reify. Although what constitutes a "significant common feature" is difficult to specify precisely, there are many clear-cut cases. Examples include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViviZwpEbGdrcN5Y29ycA" class="cyc_term">UnaryFunction</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVi5-ZwpEbGdrcN5Y29ycA" class="cyc_term">LogicalConnective</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVj62ZwpEbGdrcN5Y29ycA" class="cyc_term">IndividualDenotingFunction</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVj6CJwpEbGdrcN5Y29ycA" class="cyc_term">GenericTimePredicate</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVj9L5wpEbGdrcN5Y29ycA" class="cyc_term">LanguageDescribingPredicate</a>. Two important specializations of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjatpwpEbGdrcN5Y29ycA" class="cyc_term">RelationshipType</a> are <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViI_pwpEbGdrcN5Y29ycA" class="cyc_term">PredicateType</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rv_hDCJwpEbGdrcN5Y29ycA" class="cyc_term">FunctionType</a>. type of relationship RelationshipType first-order collection An instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvtppU5wpEbGdrcN5Y29ycA" class="cyc_term">CollectionType</a>, and a specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNooX_CChEdaAAABQ2rksLw" class="cyc_term">FixedOrderCollection</a>. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHIBS0h_TEdaAAABQ2rksLw" class="cyc_term">FirstOrderCollection</a> is the collection of all specializations of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjaApwpEbGdrcN5Y29ycA" class="cyc_term">Individual</a> (q.v.) Notable specializations of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHIBS0h_TEdaAAABQ2rksLw" class="cyc_term">FirstOrderCollection</a> include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViq35wpEbGdrcN5Y29ycA" class="cyc_term">TemporalObjectType</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVny6pwpEbGdrcN5Y29ycA" class="cyc_term">ExistingStuffType</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvWXYgJwpEbGdrcN5Y29ycA" class="cyc_term">ExistingObjectType</a>. FirstOrderCollection type of thing Collection A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjl_ZwpEbGdrcN5Y29ycA" class="cyc_term">SetOrCollection</a> (q.v.). This is the collection of all collections of things. Each <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAzJwpEbGdrcN5Y29ycA" class="cyc_term">Collection</a> is a kind or type of thing whose instances share a certain property, attribute, or feature. For example, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVkFc5wpEbGdrcN5Y29ycA" class="cyc_term">Cat</a> is the collection of all and only cats, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwOckfJwpEbGdrcN5Y29ycA" class="cyc_term">BinaryFunction</a> is the collection of all and only functions taking two arguments. The notion of collection is fundamental to the Cyc ontology, and is thus difficult to define in a precise and substantive way. But it is instructive to compare it to the mathematical notion of a set (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvl2en5wpEbGdrcN5Y29ycA" class="cyc_term">Set_Mathematical</a>). Like a set, a collection is an <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rpJ-nSEkJQdeC8NLkYPDBBw" class="cyc_term">AbstractThing</a> (i.e. aspatial and atemporal) that is not an <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjaApwpEbGdrcN5Y29ycA" class="cyc_term">Individual</a> (cf.), but instead has elements (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwGWaK5wpEbGdrcN5Y29ycA" class="cyc_term">elementOf</a>). Unlike a set, however, the elements or "instances" (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViBBJwpEbGdrcN5Y29ycA" class="cyc_term">isa</a>) of a given collection can vary from context to context, and it is possible for distinct collections to have exactly the same elements (i.e. to have the same <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwN2YGZwpEbGdrcN5Y29ycA" class="cyc_term">extent</a>) with respect to a given context. For example, the (non-reified) collections "Chordate" and "Renate" are co-extensional in the context of the present-day actual world, but have differring extents with respect to hypothetical contexts in which there exist creatures having hearts but not kidneys. This difference is sometimes summarized by saying that sets are "extensional" things and collections are "intensional" things. Many, though by no means all, of the collections reified in the Cyc ontology correspond to natural kinds or classes. It is particulary useful to reify collections that are difficult to define precisely, but about which there are many common-sense rules and other things to state. For example, it would not be worthwile to introduce a constant 'WhiteCat', both because it's easy to define the collection of white cats in terms of more general, already-reified notions (e.g. '(<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwEcGC5wpEbGdrcN5Y29ycA" class="cyc_term">CollectionIntersection2Fn</a> <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVkFc5wpEbGdrcN5Y29ycA" class="cyc_term">Cat</a> <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rBjWwGHS-EdaAAACgyZzFrg" class="cyc_term">WhiteColor</a>)'), and because there's not much to say about that particular collection. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rsX6vHnS6EdaAAACgyZzFrg" class="cyc_term">WhiteCollarWorker</a>, on the other hand, is a good collection to have reified, as it is hard to define precisely, yet is a collection about which there are many things to say. Some of the many reified specializations of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAzJwpEbGdrcN5Y29ycA" class="cyc_term">Collection</a> are <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHIBS0h_TEdaAAABQ2rksLw" class="cyc_term">FirstOrderCollection</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwIE23ZwpEbGdrcN5Y29ycA" class="cyc_term">TimeDependentCollection</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVirnZwpEbGdrcN5Y29ycA" class="cyc_term">ObjectType</a>. type of microtheory A collection of collections. Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjm6JwpEbGdrcN5Y29ycA" class="cyc_term">MicrotheoryType</a> is a specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViA1ZwpEbGdrcN5Y29ycA" class="cyc_term">Microtheory</a>. Instances of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjm6JwpEbGdrcN5Y29ycA" class="cyc_term">MicrotheoryType</a> include the collections <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVik8ZwpEbGdrcN5Y29ycA" class="cyc_term">HypotheticalContext</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViRl5wpEbGdrcN5Y29ycA" class="cyc_term">GeneralMicrotheory</a>. MicrotheoryType A collection of collections. Every instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rbEngJGwWEdqAAAACs71DGQ" class="cyc_term">CollectionClosedUnderSpecialization</a> is a collection <code>COLL-TYPE</code> with the following property: If the collection <code>COLL</code> is an instance of <code>COLL-TYPE</code>, then for any specialization <code>SPEC</code> of <code>COLL</code>, <code>SPEC</code> is also an instance of <code>COLL-TYPE</code>. Notable examples include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVitN5wpEbGdrcN5Y29ycA" class="cyc_term">TemporalStuffType</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAzJwpEbGdrcN5Y29ycA" class="cyc_term">Collection</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViA9JwpEbGdrcN5Y29ycA" class="cyc_term">Thing</a>. collection closed under specialization CollectionClosedUnderSpecialization A collection of collections. Every instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rbEngJGwWEdqAAAACs71DGQ" class="cyc_term">CollectionClosedUnderSpecialization</a> is a collection <code>COLL-TYPE</code> with the following property: If the collection <code>COLL</code> is an instance of <code>COLL-TYPE</code>, then for any specialization <code>SPEC</code> of <code>COLL</code>, <code>SPEC</code> is also an instance of <code>COLL-TYPE</code>. Notable examples include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVitN5wpEbGdrcN5Y29ycA" class="cyc_term">TemporalStuffType</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAzJwpEbGdrcN5Y29ycA" class="cyc_term">Collection</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViA9JwpEbGdrcN5Y29ycA" class="cyc_term">Thing</a>. collection closed under specialization CollectionClosedUnderSpecialization VariedOrderCollection A <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvtppU5wpEbGdrcN5Y29ycA" class="cyc_term">CollectionType</a> and the collection of all and only those <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAzJwpEbGdrcN5Y29ycA" class="cyc_term">Collection</a>s some of whose instances (or instances of instances, or instances of instances of instances, etc.) are of different "orders", where order is understood as follows. Let <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjaApwpEbGdrcN5Y29ycA" class="cyc_term">Individual</a>s be "zeroth-order" things, collections of (only) <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjaApwpEbGdrcN5Y29ycA" class="cyc_term">Individual</a>s "first-order", ..., and collections of (only) Nth-order things "(N+1)th-order". A more precise, recursive definition, then, is: a collection COL is an instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNs-F0CChEdaAAABQ2rksLw" class="cyc_term">VariedOrderCollection</a> if and only if COL has instances INST1 and INST2 such that either (i) INST1 and INST2 are of two different fixed orders N1 and N2, (ii) INST1 is of the fixed order N1 and INST2 is a varied-order collection, or (iii) INST1 and INST2 are both varied-order collections. For example, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rpJ-nSEkJQdeC8NLkYPDBBw" class="cyc_term">AbstractThing</a> is a varied-order collection since it contains both (zeroth-order) abstract individuals and (higher-order) collections. Other instances of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNs-F0CChEdaAAABQ2rksLw" class="cyc_term">VariedOrderCollection</a> include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjjo5wpEbGdrcN5Y29ycA" class="cyc_term">Intangible</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAzJwpEbGdrcN5Y29ycA" class="cyc_term">Collection</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvtppU5wpEbGdrcN5Y29ycA" class="cyc_term">CollectionType</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViA9JwpEbGdrcN5Y29ycA" class="cyc_term">Thing</a>. Note that (by clauses ii and iii) any generalization of a varied-order collection is varied-order; and (by clause iii) any (non-empty) specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNs-F0CChEdaAAABQ2rksLw" class="cyc_term">VariedOrderCollection</a> is varied-order. Note that <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNooX_CChEdaAAABQ2rksLw" class="cyc_term">FixedOrderCollection</a> (q.v.) and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNs-F0CChEdaAAABQ2rksLw" class="cyc_term">VariedOrderCollection</a> do _not_ constitute a partition of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAzJwpEbGdrcN5Y29ycA" class="cyc_term">Collection</a>: since the notion of order described above is not applicable to sets, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvl2en5wpEbGdrcN5Y29ycA" class="cyc_term">Set_Mathematical</a> (e.g.) and its specializations are neither fixed-order nor varied-order collections. variable-order Cyc collection